Relative risk regression models are being increasingly use in the analysis of cancer epidemiologic and clinical date. The statistical properties of these models in small to moderate-sized data sets are not well understood. The first part of this grant application will investigate procedures for inference, methods of model criticism and validation, and computational considerations when using general relative risk regression models for analysis of epidemiologic or clinical data. An important feature of this research will be the systematic use of the newly developed tools of differential geometry in statistics. The second part of the grant proposal will address the problem of quantitative cancer risk assessment. A previously developed stochastic two-stage model for carcinogenesis will be extended to allow the incorporation of time- dependent covariates. The properties of this model will be investigated within the context of risk assessment.